Estimation of Population Divergence Times from Non

Transcription

Estimation of Population Divergence Times from NonOverlapping Genomic Sequences: Examples from Dogs and
Wolves
Pontus Skoglund,* Anders Götherström, and Mattias Jakobsson
Department of Evolutionary Biology, Uppsala University, Uppsala, Sweden
*Corresponding author: E-mail: [email protected].
Associate editor: Rasmus Nielsen
Abstract
Key words: population divergence, demographic inference, domestic dogs, shotgun sequencing, ancient DNA.
Introduction
Methods for reconstructing the demographic history and
divergence of relatively undifferentiated populations have
attracted great interest in the last few decades, but these
methods are presently facing a number of challenges ranging from sheer computational problems to issues with data
quality and magnitude (Nielsen and Beaumont 2009).
Although recent advances in sequencing technology have
enabled retrieval of genomic sequences from several extinct mammals (e.g., Poinar et al. 2006; Noonan et al.
2006; Blow et al. 2008; Miller et al. 2008), rigid population
genetic analyses of multiple loci have so far been restricted
to Neanderthals (Noonan et al. 2006; Green et al. 2006; Wall
and Kim 2007; Green et al. 2010) and a single modern
human (Rasmussen et al. 2010), and direct genomic analysis of extinct populations has yet to fulfill its full promise
to shed light on past population processes (Willerslev and
Cooper 2005; Millar et al. 2008; Green et al. 2009).
A major problem for ancient DNA (aDNA) studies stems
from the fact that the most powerful approaches are based
on direct shotgun sequencing (Millar et al. 2008, but see
also Burbano et al. 2010). In most applications of direct ancient genomic sequencing, endogenous sequences will be
outnumbered by microbial DNA, making it easier to generate large amounts of data compared with targeted methods, but difficult to achieve high coverage assemblies
(Millar et al. 2008), resulting in little overlap between loci
obtained from different individuals (e.g., Green et al. 2010).
Population genetic analyses of ancient genome data can use
reference genomes (Green et al. 2010) and single-nucleotide
polymorphism (SNP) information (Rasmussen et al. 2010),
but multiple reference genomes and public SNP databases
currently only exist for a few vertebrates. As more genomic
reference data becomes available, large-scale studies will become available also for non-model organisms, and we need
clear paradigmatical approaches for analyzing paleogenomic
data that 1) allow statistical testing of explicit demographic
models (e.g., Nielsen and Beaumont 2009), 2) are resilient to
contamination problems (Gilbert et al. 2005; Wall and Kim
2007; Green et al. 2009), 3) can handle postmortem nucleotide misincorporations (Pääbo 1989; Briggs et al. 2007;
© The Author 2010. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please
e-mail: [email protected]
Mol. Biol. Evol. 28(4):1505–1517. 2011 doi:10.1093/molbev/msq342
Advance Access publication December 21, 2010
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from http://mbe.oxfordjournals.org/ by guest on December 1, 2014
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article
Despite recent technological advances in DNA sequencing, incomplete coverage remains to be an issue in population
genomics, in particular for studies that include ancient samples. Here, we describe an approach to estimate population
divergence times for non-overlapping sequence data that is based on probabilities of different genealogical topologies
under a structured coalescent model. We show that the approach can be adapted to accommodate common problems
such as sequencing errors and postmortem nucleotide misincorporations, and we use simulations to investigate biases
involved with estimating genealogical topologies from empirical data. The approach relies on three reference genomes and
should be particularly useful for future analysis of genomic data that comprise of nonoverlapping sets of sequences,
potentially from different points in time. We applied the method to shotgun sequence data from an ancient wolf together
with extant dogs and wolves and found striking resemblance to previously described fine-scale population structure
among dog breeds. When comparing modern dogs to four geographically distinct wolves, we find that the divergence time
between dogs and an Indian wolf is smallest, followed by the divergence times to a Chinese wolf and a Spanish wolf, and
a relatively long divergence time to an Alaskan wolf, suggesting that the origin of modern dogs is somewhere in Eurasia,
potentially southern Asia. We find that less than two-thirds of all loci in the boxer and poodle genomes are more similar to
each other than to a modern gray wolf and that—assuming complete isolation without gene flow—the divergence time
between gray wolves and modern European dogs extends to 3,500 generations before the present, corresponding to
approximately 10,000 years ago (95% confidence interval [CI]: 9,000–13,000). We explicitly study the effect of gene flow
between dogs and wolves on our estimates and show that a low rate of gene flow is compatible with an even earlier
domestication date ;30,000 years ago (95% CI: 15,000–90,000). This observation is in agreement with recent
archaeological findings and indicates that human behavior necessary for domestication of wild animals could have
appeared much earlier than the development of agriculture.
Skoglund et al. · doi:10.1093/molbev/msq342
Materials and Methods
Genealogical Inference of Divergence
To estimate population divergence times in a four-way alignment between a sample (canid) sequence, two modern reference genomes (boxer and poodle, see below) and an
outgroup, we first infer the genealogical topology by recording each position where two of the canid sequences has a derived allele and the third retains the ancestral variant found
in the outgroup using a simple parsimony method that assumes an infinite sites model of mutation (fig. 1). If two positions in the same alignment results in different topologies,
for example due to recombination, the locus is discarded.
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We estimate the internode divergence time T (measured
in units of Ne generations, where Ne is the effective population size in chromosomes) between a sample (s) and
a corresponding population ancestral to two differentiated
populations (‘‘p’’ for poodles and ‘‘b’’ for boxers) using
probabilities of concordant or discordant topologies under
a coalescent divergence model (Hudson 1983; Takahata
1989; Rosenberg 2002). In this model, there are three possible topologies describing the genealogy of the three lineages, of which we denote the (s,(b,p)) case concordant,
and the remaining two, (b,(p,s)) and (p,(b,s)), discordant.
The probability of each discordant topology equals the
probability that p and b do not coalesce during the time
spent in the internode population (eT), where they are
unable to coalesce with s, multiplied by the probability that
s and p coalesce in the ancestral population (one-third).
The probability of the remaining concordant topology
equals 1 2eT/3. We used the log-likelihood function
of the internode divergence time T to compute the maximum likelihood estimate (MLE) of T and to obtain confidence intervals (CIs, Wakeley 2008)
2 T
2 T
logðLðTÞÞ 5 Gc log 1 e
þ Gd log e
;
3
3
where Gc is the number of concordant topologies and Gd
is the total number of discordant topologies. To plot loglikelihood functions on the same scale, we subtract the maximum value of log(L(T)) from all values to obtain a relative
log-likelihood function.
Analysis of Pleistocene Siberian Wolf Sequences
Blow et al. (2008) sequenced (Illumina and 454 GS20)
aDNA from an ancient wolf from the Altai region in Asia
(Derevianko et al. 2003), dated by thermoluminescence to
between 40 and 50 Ka). Both processed and raw data sets
from Blow et al. (2008) were kindly provided by the authors.
We initially aligned the processed Altai wolf sequences to
the boxer (Canfam2.0; Lindblad-Toh et al. 2005), poodle
(Kirkness et al. 2003), and cat (catChrV17e; Pontius
et al. 2007) genome assemblies. However, a bias in shared
allelic states with the boxer over the poodle was identified
(the Altai wolf shared a boxer-specific allele at 181 positions
but shared the poodle allele at only 1 position). Because
this effect was likely due to conservatively stringent alignment criteria to the boxer genome in the pipeline for identification of authentic canid sequences implemented by
Blow et al. (2008), we performed an independent analysis
of the 2,745,862 raw sequence reads. We used megablast
(Zhang et al. 2000) to identify canid aDNA sequences in
the raw library by aligning sequences to the three genomes
using word size 16. Sequences with bit score .35 and expect value ,0.001 were extracted, in total 97,319 reads.
These reads were then aligned to the entire NCBI ref_seq
and other_genomic databases, leaving 93.7% (91,178 reads,
mean length 40 bp, range 37–118 bp) of the originally identified reads with the best hit to a carnivore genome. This
amounts to 3.45% canid reads, compared with the 2.16%
(57,028 reads) identified by Blow et al. (2008). Comparison
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Brotherton et al. 2007; Axelsson et al. 2008) and sequencing
errors (Johnson and Slatkin 2008; Jiang et al. 2009; Lynch
2009; Liu et al. 2010), and 4) allow comparison between data
from different points in time (Depaulis et al. 2009).
We describe a method which utilizes reference genomes
for comparing multiple loci that do not overlap among
samples and allows maximum likelihood estimation of
population divergence times. To illustrate the method,
we analyzed available genomic shotgun sequences from
modern dogs (Canis lupus familiaris) and gray wolves
(Canis lupus lupus) together with an ancient wolf to investigate the origin of dog domestication. Although it is clear
that the closest living relatives of domestic dogs are Eurasian gray wolves (Olsen 1985; Clutton-Brock 1987; 1995;
Vilà et al. 1997, 1999, Leonard et al. 2002), the timing
and process of domestication remain contentious (e.g.,
Morey 2006; Boyko et al. 2009; Pang et al. 2009; vonHoldt
et al. 2010). Initial analyses of mtDNA yielded estimates of
a first domestication more than 100 thousand years ago
(Ka) (Vilà et al. 1997), but recent phylogeographic mtDNA
studies claim a date less than 16,300 years ago (Savolainen
et al. 2002, Pang et al. 2009; but see also Boyko et al. 2009).
Population genetic analyses using multiple autosomal loci
have also produced disparate estimates, corresponding to
10–27 Ka depending on assumptions about generation
time (Lindblad-Toh et al. 2005; Gray et al. 2009) and has
pinpointed the Middle East as the most likely region of origin (vonHoldt et al. 2010). The archaeological record of
dogs has pointed to a more recent domestication time
based on fossils and burials ;12,000–14,000 years old
(Davis and Valla 1978; Nobis 1979; Musil 1984; Olsen
1985; Benecke 1987; Sablin and Khlopachev 2002; Morey
2006), but a recent study documents dog-like morphological features in European canid fossils as old as 31,000 years
(Germonpré et al. 2009).
Using our approach, we estimate that dogs and wolves
first diverged more than 10 Ka, and that postdivergence
gene flow is compatible with an even more ancient divergence date. We investigate possible biases arising from sequencing error, nucleotide misincorporations, sequence
alignment, short fragment length, time-structured sampling, and incomplete genealogy information and show
that our approach could be particularly useful for analyzing
multilocus aDNA sequence data.
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Nonoverlapping Data and Population Divergence Times · doi:10.1093/molbev/msq342
A
T
G
C
0.10
0.2
0.3
0.4
0.5
Relative base frequency
0.6
B
0.1
Fraction C to T mismatches
A
0.40
To identify homologous regions, identified endogenous sequence reads from the Altai wolf were realigned to the
boxer, cat, and poodle genome assemblies. Megablast
searches used the option ‘‘word size’’ set to 12, ‘‘culling
limit’’ set to 20 and ‘‘e-value’’ 5 0.001. In addition, trace
reads from an Alaskan gray wolf (n 5 21,687), Chinese gray
wolf (n 5 23,410), Indian gray wolf (n 5 22,539), Spanish
0.30
Alignment of Modern and Ancient Data to
Carnivore Genomes
gray wolf (n 5 22,116), German shepherd (n 5 99,981), English shepherd (n 5 99,373), Labrador retriever (n 5 99,698),
Beagle (n 5 99,648), Alaskan malamute (n 5 99,829),
Rottweiler (n 5 99,983), Bedlington terrier (n 5 98,208),
Portuguese water dog (n 5 98,112), and Italian greyhound
(n 5 98,320), originally published by Lindblad-Toh et al.
(2005), were downloaded from the NCBI trace archive
and aligned in a similar way as the Altai wolf. Because
the majority of these sequences were .800 bp, word size
was set to 40 and 24 for searches of wolf sequences against
the dog and cat genomes, respectively. Matches were required to align over at least 30 bases and hits to the two
dog genomes had to cover .50% of the read length to
be retained. The best alignment to each genome was identified as the hit which had the highest bit score and in case
of several hits with equal score, the longest alignment was
considered the best. Multiple alignment of a canid sequence
0.20
of these sequences with the boxer reference genome revealed patterns of molecular degradation characteristic
for aDNA (fig. 2; Briggs et al. 2007). Additionally, the bias
of sharing alleles with the boxer more often than the poodle was now similar to that in modern wolf sequences
of similar fragment length (133 and 35, respectively, see
below).
10
20
30
Distance from 5' end of sequence read
40
−10
−5
0
5
10
Distance from 5' end of sequence read
FIG. 2. Signs of molecular degradation in the Altai wolf sequences. (A) Increased frequency of C / T mismatches compared with other
mismatches toward the 5’ end of the sequence read (B) biased base composition in the reference sequence at the 5’ end of the aligned
sequence read.
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FIG. 1. Illustration of the model used for estimating divergence times from counts of different gene genealogy topologies. (A) A model of dog
demographic history with the internode population and the ancestral population indicated. (B) The concordant genealogical topology with the
internal branch indicated. (C) One of two possible discordant topologies with the internal branch indicated.
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and its best aligned sequence in each target genome were
created using MUSCLE v3.7 with default parameters (Edgar
2004). In all downstream evolutionary analyses, we excluded
indels due to uncertainties about the mutation rate and positions where one of the sequences had a low-quality base
(Lindblad-Toh et al. 2005). In the topological analysis and
estimates of pairwise mismatches involving the ancient wolf,
we excluded C / T and G / A mismatches between sample sequence and reference genome because these mismatches are most likely due to postmortem nucleotide
misincorporations.
Estimation of Sequencing and Alignment Error
Rates
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B 5 E ð1 Dc b Þ E Dc b
3
rearranging and solving for E gives
E5
3B
:
3 4Dc b
Correcting Genealogical Topologies for Sequencing
and Alignment Error
Using the estimates of the error rate, we computed the
fraction of sites f in the sample that erroneously display
an ancestral (cat) allele, due to sequencing or alignment
errors, in three-way alignments of the sample, the boxer
and the cat. These events only occur at sites where the
boxer and cat differ (Dcb) and must confer a change from
the boxer variant to the particular variant present in cat
(happens in one-third of the cases), in total
f 5 E Dc b 1
:
3
We used the high-quality boxer sequence to compute f but
note that the lower-quality poodle data could also have been
used for this analysis. Next, we used the average length of
alignments in base pairs (L) to compute the expected occurrence F 5 ( f L) of such sites in an alignment. It is possible to
have F 1 for long alignments, but because our empirical data
only consisted of relatively short alignments, which typically
had one or very few variable sites, we can assume that F , 1
for each alignment and treat F as a probability that a locus
displays a concordant site due to an error.
We computed the number of loci that erroneously display a concordant topology assuming that we can estimate
this proportion from (1) the observed number of concordant loci NCO, which is composed of both true concordant
loci (NCT) and loci without true informative sites that have
been assigned as concordant due to the concordant sites
arising from errors (NNT F), NCO 5 NCT þ NNT F, and
(2) the observed number of noninformative loci NNO, from
which a fraction has been erroneously moved to the concordant category, NNO 5 NNT (1 F). Using these two
relationships, we obtained a corrected number of concordant loci NCT as
NCT 5 NCO NNO
F:
1F
We also applied a correction to the number of observed discordant topologies; because if a sequencing error converts
a derived variant to an ancestral variant, it might also cause
the appearance of a concordant site in loci that are discordant. If the locus contains sites supporting the true topology
(i.e., discordant), this type of error would cause the locus to be
discarded due to violating the assumption that sequence regions are free from recombination. The number of observed
Using a rather distantly related outgroup genome, such as
the cat, to infer the ancestral allelic state introduces a potential source of bias in that sequencing or alignment errors
in the shotgun sequences not only inflates the length of the
external branch but may also occur on a site that differs
between canids and cats, changing the state in the canid
to the ancestral variant found in the cat genome. These
types of errors could result in the topology of a locus to
be incorrectly inferred as ‘‘concordant’’ or ‘‘discordant’’ using our parsimony method. We therefore estimated the
rate of sequencing and alignment errors present in the
modern shotgun sequences using an approach that is
based on assuming a constant mutation rate and implemented a correction to our inference method. Specifically,
we used the observed differences between the boxer and
cat genomes, both relatively high-quality genomes, to set
a baseline for expected canid-felid pairwise differences to
which the modern shotgun sequences can be compared
(e.g., Burgess and Yang 2008). We considered the exact
same positions as those used for the genealogical inference
procedure. For example, in the alignments constructed as
described above between Chinese wolf, cat, boxer, and poodle sequences, the boxer and cat sequences differ at 14.86%
(Dcb 5 0.1486; 95% CI from 10,000 bootstrap replicates:
0.1475–0.1497) of the positions. Due to the high quality of
the genomes, we consider this level of differences to be
the ‘‘true’’ level of differences between canids and cat, unaffected by errors. However, for the same positions, the
Chinese wolf (the sample) differs from the cat at 15.70%
(Dcw 5 0.1570; CI: 0.1560–0.1582), and the additional
fraction (0.84%) differing sites between the cat and the
sample (B) can be caused by alignment or sequencing errors due to the lower quality of the single-pass sequences of
the Chinese wolf. Errors that occur in positions where the
sample (the Chinese wolf in this example) and the cat have
the same true variant (fraction 1 Dcb) will always be
visible and increase the observed difference. Those errors
that occur on true polymorphic sites (between sample
and cat) can change the sample variant to another variant
(not the cat variant; happens in two-thirds of the cases),
which does not change the number of polymorphisms,
or the error can change the sample variant to the same
variant as the cat (happens in one-third of the cases), decreasing the observed difference between the cat and the
sample. Assuming that the number of errors in the boxer
and the cat reference genomes are negligible and that errors only hit a site once, an expression for the contribution
by the error rate E to the additional fraction of differing
sites between the cat and the sample B is
discordant loci (NDO) should therefore equal the number
of true discordant loci (NDT) that do not contain sites that
erroneously display a concordant topology, NDO 5 NDT (1 F). The true number of discordant loci would then be
computed as
NDT 5
NDO
:
1F
In the above analysis, we focused on the observation of erroneous ancestral alleles and not the observation of erroneous
derived alleles because erroneous derived alleles only influence our analysis if they appear at sites where the two canids
already have different alleles. Because the fraction of polymorphic sites between two canids is approximately 0.1%
(Lindblad-Toh et al. 2005) and the fraction of polymorphic
sites between a cat and a canid is approximately 15% (see
below), the potential error due to erroneous derived alleles
is negligible compared with the effect of erroneous ancestral
alleles.
To compare our method for population divergence time
estimation with a different approach, we computed average sequence coalescence time (average time to most recent common ancestor [TMRCA]) between the boxer and
our sample sequences using the same positions as above.
We used a method where the error-prone polymorphisms
specific to low-coverage shotgun sequences can be excluded by computing the average number of mutations
on the fraction of the branch between the boxer and
cat that postdate the TMRCA of the boxer and the sample
sequence (Noonan et al. 2006; Green et al. 2006, 2010;
Prüfer et al. 2010). We computed a statistic Ss which we
define as the number of sites where the sample sequence
‘‘s’’ shares an (ancestral) allele with the cat but the boxer
has a different (derived) allele, divided by the total number
of investigated positions. In a standard neutral coalescent
model without population structure, this value would correspond to the population mutation rate h 5 4Nel, such
that Ss 5 h/2, because only mutations on one of the
branches in the genealogy of the boxer and the sample
are considered. In the case of population divergence, Ss
is equal to (h þ T)/2, where T is the divergence time between populations.
To correct for the effect of sequencing and alignment
errors when using an outgroup as distant as the cat (see
above and Prüfer et al. 2010), we used the relatively
high-quality (but lower coverage than the boxer) poodle
sequences. We based the error correction on the assumption that the poodle sequences and sequences from other
modern European dog breeds should have approximately
the same value of Ss and that any remainder can be attributed to errors (note that this procedure is different from
the error correction applied to the genealogical approach
above). First, we computed the fraction of differences between the boxer and the cat in which the poodle carries the
cat allele, Sp 5 0.000668. The average for other modern dog
breed sequences was Sd 5 0.001270 (excluding the Alaskan
Malamute), and assuming that all low-coverage Sanger
shotgun sequences from Lindblad-Toh et al. (2005) had identical inflation in sequencing error, we quantified the inflation
due to errors as ID 5 Sd Sp 5 0.000601. We then estimated
the average value for wolves (Sw 5 0.001724) and subtracted
the estimated inflation due to sequencing errors (ID), resulting
in a corrected Sw 5 0.001122. By normalizing this estimate of
Sw with the corrected average for European dogs (Sw/Sd), we
obtain an estimate of the relative average TMRCA between
a modern dog chromosome and a modern wolf chromosome
that is independent of assumptions about the mutation rate,
other than the mutation rate being equal for all lineages. Because the Altai wolf sequences is from a different historical
time and sequenced with a different technology (short sequences), we computed SAltai/Sd without error correction.
Bootstrap Analysis
We obtained 95% bootstrap CIs for the fraction of concordant topologies, Ss, Sw/Sd and E from 10,000 pseudoreplicates over loci. These CIs reflect the amount of sampling
error involved in each estimate. Note that the uncertainty
for the estimates of the error rate E (the CIs are narrow, see
below) is not carried through to the other estimates which
involve E and therefore represents a potential additional
source of uncertainty.
Simulations
We generated gene genealogies using Serial Sim-Coal
(Excoffier et al. 2000; Anderson et al. 2005) and placed mutations on the genealogies with probability proportional to
branch length using a custom program (available upon request). For 100,000 simulated genealogies, we sampled the
number of segregating sites from a Poisson distribution
with mean equal to the total genealogy length (Hudson
1990), assuming a 500-bp locus with mutation rate of
108 per bp and generation (reasonable for dogs, see,
e.g., Lindblad-Toh et al. 2005). For each particular demographic model, we calculated the proportions of concordant and discordant genealogies from informative
segregating sites and relative average TMRCA (Sw/Sd) between dogs and wolves with analogous procedures as for
the empirical data. For all models, we assume breed creation
70 generations ago with no migration between breeds
(Wayne and Ostrander 2007), in which case Ne of breeds
has no affect on our analysis. Based on previous estimates,
we set the ancestral dog effective population size to 13,000
chromosomes (Lindblad-Toh et al. 2005), the wolf effective
population size to 45,000 chromosomes (Gray et al. 2009),
and generation time to 3 years (Lindblad-Toh et al. 2005;
Gray et al. 2009). We investigated the effect of very low
(Nem 5 0.25) and low (Nem 5 0.5) symmetric migration
rates between dogs and wolves. For testing scenarios involving the Altai wolf, we used 500,000 replicates and a locus
mutation rate of 3.5 107 (corresponding to a 35-bp sequence with a mutation rate of 108 per bp and generation),
an age of 13,000 generations for the Altai wolf, a dog-wolf
divergence time of 5,000 generations ago without gene flow,
and assumptions about Ne in dogs and wolves as above.
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Average Sequence TMRCA between Canids
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0.8
0.7
0.6
0.5
1 segr. site, R = 0.1
1 segr. site, R = 1
1 segr. site, R = 10
True topology
0
1
2
3
4
5
T
FIG. 3. The bias in the observed fraction of concordant genealogies
inferred from SNPs depends on the effective sizes of ancestral and
internode populations. The fraction of concordant topologies as
a function of divergence time (T) given by directly counting the
topologies from simulations is shown as a solid line and the fraction
of concordant topologies obtained when inferring the topology
from a single segregating site are shown as broken lines. Results
from three models assuming different ratios (R 5 Na/Ni) between
the ancestral effective population size (Na) and the internode
effective population size (Ni) are shown (R 5 0.1, 1, and 10).
Divergence time (T) is shown in units of Ni generations.
We investigated this bias using coalescent simulations
for different ratios (0.1, 1, and 10) of ancestral effective population size Na and internode effective population size Ni.
We placed a single segregating site on the genealogy and
compared the proportion of observed concordant genealogies based on the information provided by SNPs and the
true proportion of concordant topologies. The simulations
show that a proportionally larger effective size of the ancestral population does indeed result in a lower bias (fig. 3).
Because sequences in empirical data do not always contain
exactly one SNP, we investigated the bias when using 500bp sequences (similar to the average alignment length in
our data) and our model of dog demographic history
(see Materials and Methods). By comparing the true fraction of concordant topologies and the fraction of concordant topologies computed from sequence data, we
estimate the bias to less than 3% (fig. 4).
Divergence between Dogs and Wolves
Using 4,085 alignments (599–1,475 from each of four
wolves) of autosomal wolf and dog sequences that had informative sites which could be used to determine the topology of the genealogy, we found that 49–58% of all loci
display the concordant topology for the poodle and boxer
compared with the wolf (table 1). This fraction was similar
for all three Eurasian gray wolves from India (49.5%, 95%
bootstrap CI: 47.0–52.0%), China (50.8%, CI 48.1–53.5%),
and Spain (51.2%, CI: 47.1–55.0%) but higher for the individual from Alaska (57.5%, CI: 53.5–61.4%). We computed
the likelihood of divergence times given the sequence data
and find MLEs of T from 0.28 to 0.45 coalescent time units
(table 1 and fig. 5A), between modern European dogs (poodle and boxer) and each of the wolves. Assuming that all
To estimate the divergence time T between the ancestral
population of the boxer and poodle and the population
leading to a particular canid sample of interest, we used
a coalescent-based approach based on the number of gene
genealogies that show a discordant topology and the number of gene genealogies that show a concordant topology,
when compared with the population topology (Takahata
1989; Rosenberg 2002; Wakeley 2008). The number of concordant and the number of discordant topologies allow us
to compute the likelihood for different divergence times
(scaled by generation time and effective population size
Ne) assuming no migration between populations and assuming that loci are independent of each other (see
Materials and Methods).
This framework has the inherent assumption that the
true genealogy is always known for any given locus (Wakeley
2008). However, in practice, the method requires that the
genealogical topology is inferred using genetic markers, a step
which can potentially give rise to biased results (Nielsen
1998; Yang 2002). In our implementation, we assume an
infinite sites mutation model and reconstruct a genealogical topology only when sufficient information is available
from SNPs in the sequence alignments. For a mutation to
be informative about the genealogy in this parsimony
framework, it must occur on an internal branch of the
genealogy (excluding the internal branch leading to the
outgroup). This confers a possible bias if one category of
topology is more likely to contain sufficient information
for inferring the genealogy. Specifically, if one category
of topology has, on average, genealogies with longer internal branches, the genealogies in this category would more
often contain informative sites than a topology category
where genealogies have short internal branches. In our divergence model, the concordant topology can arise when
lineages sampled from the two more closely related populations coalesce either in the ancestral population of these
two populations (the ‘‘internode’’ population) or in the ancestral population of all three populations (fig. 1). We can
think of the genealogy as consisting of two parts: the part
before the final ancestral population and the part where all
remaining lineages are in the final ancestral population. The
portion of genealogies that have a concordant topology
that have arisen through a coalescent event prior to reaching the final ancestral population have a longer internal
branch on which informative genealogies can arise than
concordant or discordant topologies that are formed when
all three lineages reach the ancestral population. This results in a higher probability of detecting concordant topologies. The magnitude of this bias will depend on the
effective sizes of the internode and ancestral populations
because a reduction in effective size in the ancestral population leads to a higher probability of rapid coalescence,
resulting in a smaller portion of the total branch length due
to lineages in the ancestral population.
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Investigating the Effect of Incomplete Genealogy
Information
Fraction concordant topologies
Results
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1.0
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Table 1. Summary of Data and Divergence Time Estimates (corrected for potential sequencing and alignment errors).
Number of Average base
Inferred
Alignments pair /Alignment Topologies
Altai wolf
7,655
35
841
Alaska wolf
2,287
563
637
Spanish wolf
1,992
627
599
Chinese wolf
5,067
501
1,311
India wolf
5,606
495
1,475
Alaskan malamute
19,302
539
4,564
Italian greyhound
19,436
540
4,480
Beagle
20,414
538
4,876
German shepherd
26,388
495
6,093
Rottweiler
20,940
540
4,933
Portuguese water dog
18,747
524
4,212
Bedlington terrier
20,117
542
4,720
English shepherd
20,014
539
4,325
Labrador retriever
27,739
512
5,637
Fraction Concordant
Topologies (95%
Bootstrap CI)
80.0% (77.2–82.7%)
57.5% (53.5–61.4%)
51.2% (47.1–55.0%)
50.8% (48.1–53.5%)
49.5% (47.0–52.0%)
34.1% (32.7–35.5%)
33.8% (32.5–35.2%)
33.7% (32.4–35.0%)
32.6% (31.5–33.8%)
32.3% (31.0–33.6%)
32.6% (30.8–33.7%)
31.8% (30.5–33.1%)
28.5% (27.2–30.0%)
21.8% (20.7–22.9%)
a wolf compared with the TMRCA between two dogs
and is independent of mutation rate. For comparison,
Lindblad-Toh et al. (2005) estimated average pairwise differences to ;1/900 between European dogs and ;1/578 between a boxer and a wolf, corresponding to Sw/Sd 5 1.56.
Because backcrossing between dogs and gray wolves still
occurs in sympatric regions and may have been even more
frequent in the past (Vilá et al. 2005; Wayne and Ostrander
2007), making inferences based on a model with complete
isolation of dogs and wolves might underestimate divergence times. To investigate the impact of migration on
our estimates of T, we simulated genetic data using a population divergence model with migration (see Materials
and Methods). We qualitatively assessed the ability of different assumptions on migration rate and divergence time
to reproduce the genealogical concordance and Sw/Sd in
our empirical data. Barring migration between the dog
and wolf populations, genealogical concordance (estimated from sequences) corresponding to 49.5% (observed
value for the Indian wolf, CI: 47.0–52.0%) can readily be
explained by a domestication ;10,000 years ago (3,500
B
Nem = 0.25
1.0
1.0
N em = 0
0.9
one segr. site
500 bp sequence
true topology
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
one segr. site
500 bp sequence
true topology
0.4
A
Reference
Blow et al. (2008)
Lindblad-Toh et al. (2005)
0
10000
20000
30000
40000
Divergence time (years)
50000
0
10000
20000
30000
40000
50000
FIG. 4. The bias for observing concordant topologies due to incomplete genealogy information for (A) a model of dog demographic history
without migration and (B) a model with migration. The fraction of concordant topologies estimated from a single segregating site is shown as
a dotted line, the fraction estimated from a 500-bp locus with a mutation rate of 108 per bp and generation is shown as a dashed line and the
true fraction of concordant genealogies is shown in as a solid line.
1511
sequences represent independent samples from one population, these sequences can be analyzed jointly using our
approach. Combining the sequence data for all Eurasian
gray wolves (excluding the Alaskan wolf) resulted in an estimated divergence time of 0.29 (maximum likelihood CI:
0.26–0.33) (fig. 5B).
For comparison, we also used a different method that estimates the TMRCA between sequences rather than population divergence times (Green et al. 2006; Noonan et al.
2006). This method proceeds by computing the fraction
of pairwise differences that have occurred on the boxer lineage since the TMRCA, thus ignoring polymorphisms unique
to the shotgun sequences. Setting the cat–dog ancestor to 55
million years ago (Pontius et al. 2007), the mean TMRCA between the boxer and the poodle is ;36,700 years ago and
between the boxer and wolves ;61,800 years ago. Because
this value is heavily dependent on the assumed canid-felid
divergence and a clock-like mutation rate, we normalized
the Sw statistic with the value for dogs Sd (see Materials
and Methods) and obtained Sw/Sd 5 1.70 (CI: 1.64–1.77). This
statistic reflects the relative TMRCA between a dog and
Divergence Time
T MLE (95%
maximum likelihood CI)
1.21 (1.07 to 1.35)
0.45 (0.36 to 0.54)
0.31 (0.23 to 0.40)
0.30 (0.25 to 0.36)
0.28 (0.23 to 0.33)
0.011 (–0.009 to 0.032)
0.007 (20.013 to 0.029)
0.005 (20.014 to 0.025)
20.01 (20.027 to 0.008)
20.015 (20.034 to 0.005)
20.016 (20.036 to 0.005)
20.023 (20.042 to 20.003)
20.07 (20.09 to 20.05)
20.16 (20.17 to 20.15)
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Table 2. Pairwise Differences, Error Estimates, and Di Divergence Time Corrections.
India wolf
Spanish wolf
Chinese wolf
Alaska wolf
Alaskan malamute
English shepherd
German shepherd
Rottweiler
Italian greyhound
Labrador retriever
Bedlington terrier
Beagle
Portuguese water dog
Standard Poodle
0.00181
0.00177
0.00172
0.00159
0.00140
0.00133
0.00130
0.00130
0.00129
0.00126
0.00125
0.00124
0.00122
0.00067
S
(0.00174–0.00189)
(0.00167–0.00188)
(0.00165–0.00180)
(0.00150–0.00169)
(0.00137–0.00144)
(0.00130–0.00136)
(0.00127–0.00133)
(0.00126–0.00139)
(0.00125–0.00132)
(0.00123–0.00129)
(0.00122–0.00128)
(0.00121–0.00127)
(0.00119–0.00125)
(0.00066–0.00078)
1.81
1.74
1.67
1.48
1.20
1.08
1.04
1.04
1.02
0.98
0.97
0.96
0.92
Ss/Sp
(1.71–1.92)
(1.60–1.91)
(1.56–1.79)
(1.35–1.63)
(1.15–1.25)
(1.04–1.14)
(1.00–1.09)
(0.99–1.09)
(0.98–1.07)
(0.94–1.02)
(0.93–1.02)
(0.91–1.00)
(0.87–0.97)
1.00
0.01110
0.01078
0.01054
0.01003
0.01011
0.01024
0.00832
0.00907
0.00920
0.00946
0.00858
0.00833
0.00836
0.00014
E
(0.01060–0.01163)
(0.01008–0.01152)
(0.01004–0.01105)
(0.00949–0.01059)
(0.00991–0.01031)
(0.01005-0.01044)
(0.00814–0.00849)
(0.00891–0.00923)
(0.00901–0.00940)
(0.00927–0.00965)
(0.00841–0.00876)
(0.00815–0.00850)
(0.00818–0.00853)
(0.00008–0.00019)
NCO2NCT (%)
27.70
27.90
26.40
20.80
35.80
40.70
32.60
34.30
34.40
44.00
33.70
31.70
33.00
NA
S is the fraction of differences per site between the boxer and the cat in which the sample sequence carries the cat allele, Ss / Sp is the corrected estimate of the relative
TMRCA between the sample and the boxer genome normalized by the estimate for poodle sequences, E is the estimated frequency of sequencing/alignment errors per
bace pair, NCO – NCT is the difference between the fraction of concordant topologies before and after error correction. Bootstrap CIs (95%) obtained from 10,000 pseudoreplicates over loci are shown in parentheses.
Divergence between the Ancient Altai Wolf and
Modern Canids
Sequences from the ancient Altai wolf displayed a fraction
of 80.0% concordant genealogies with respect to the modern dog genomes (CI: 77.2–82.7%). This corresponds to an
MLE of T 5 1.21 (CI: 1.07–1.35), which is, compared with
the estimate of the modern gray wolf–dog divergence, approximately four times as far back in time (fig. 5B). We also
investigated possible divergence times using simulations.
Our results indicate a divergence between the Altai wolf
and the wolf population ancestral to dogs approximately
90,000 years ago (CI: 75,000–110,000, fig. 7). These simulations also illustrate that if the ancient sample is from a population that is directly ancestral to the modern
populations, the fraction of concordant topologies corresponds directly to the age of the ancient specimen
(fig. 7A). In addition, we obtained a SAltai/Sd statistic of
3.81 (CI: 3.52–4.10), which together with the high divergence estimate indicates that the Altai wolf has a significantly deeper divergence to modern dogs than the
modern gray wolves in our data set.
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It has previously been shown that sequence read length
can bias sequence comparisons between genomes (Green
et al. 2009). To investigate the sensitivity of our estimates to
fragment length, with special regard to the short read
length produced by the Illumina technology used in the
Altai wolf study (Blow et al. 2008), we created artificially
fragmented data sets from the modern wolf sequences with
sizes corresponding to the typical range of aDNA (35–250
bp). We found that data sets with short fragment length
tend to have a lower uncorrected fraction of concordant
topologies, resulting in underestimation of divergence
times, but note that the error correction alleviates this bias
(fig. 8A). In contrast, short fragment length has a tendency
to increase the estimate of relative TMRCA (fig. 8B and
Green et al. 2009). The bias for the uncorrected fraction
of concordant topologies could be due to short fragments
more frequently being mapped to an incorrect location in
one of the two dog genomes but not the other, causing an
incorrectly scored discordant topology. Indeed, a bias in the
uncorrected analysis where the discordant topology that
has the poodle lacking a canid-specific allele (found in wolf
and boxer) over the discordant topology where the boxer
lacks the canid-specific allele increased for short fragment
lengths (Fig. 8C). A possible explanation for this is that
short reads are more prone to align to a nonhomologous
region in the lower-quality 1.5 poodle genome. Regardless, this bias would imply a possible underestimation of the
divergence time for very short reads, supporting the conclusion that the Altai wolf is from a population distantly
related to modern dogs.
Divergence between Dog Breeds
For the nine dog breeds, a range of 4,212–5,637 alignments
showed informative sites that could be used to determine
the topology of the gene genealogies (table 1). Using our
approach based on discordant/concordant gene genealogies, we estimated the population divergence between
the ancestral population of boxers and poodles and the
other breeds as follows: Labrador retriever, 0.16; English
generations, CI: 9,000–13,000 years). However, assuming
a low migration rate (Nem 5 0.25) between dogs and
wolves from T to the creation of breeds pushes the domestication time to ;30,000 years ago (CI: 15,000–90,000) (fig.
6A). The two models with migration affect the Sw/Sd statistic in a similar way, but we found that the assumption of
a three to four times larger wolf effective population size
compared with dogs (see Materials and Methods) is not
enough to reproduce the above estimated divergence time
and Sw/Sd values for the Indian wolf under our model (fig.
6B), but note that Sw/Sd for the three other wolves was
slightly lower (table 2). A greater difference between the
effective population sizes of wolves (Nw) and dogs (Nd)
would make the simulation results more similar to our observations because TMRCAs between populations are increased by both divergence time and ancestral effective
size.
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shepherd, 0.07; Bedlington terrier, 0.02; Portuguese water dog, 0.02; Rottweiler, 0.01; German shepherd, 0.01;
Beagle, 0.01; Italian greyhound, 0.01; and Alaskan Malamute, 0.01 coalescent time units (table 1). The observation
of negative divergence times is not entirely unexpected
considering that the boxer and poodle belonged to separate population clusters in previous studies (e.g., Parker
et al. 2004, 2007; vonHoldt et al. 2010). A closer relationship
of a sample dog breed to either the boxer or the poodle is
a violation of the assumed population topology in our
method. Although in principle the population topology
can be chosen that maximizes the number of concordant
topologies, our error correction method considers the two
discordant topologies jointly. However, in our basic model,
negative divergence times could be interpreted as relative
to the divergence time of boxer and poodle populations,
with time scaled in units appropriate to historical effective
population size fluctuations. The rank order of inferred divergence times corresponds roughly to four previously suggested higher-order groups: ‘‘Modern European/Hunting,’’
‘‘Mastiff-type,’’ ‘‘Herding,’’ and ‘‘Asian/Ancient’’ (fig. 5A;
Parker et al. 2004; Wayne and Ostrander 2007). For instance,
we retrieve a separation of the Alaskan Malamute (Asian/
Ancient) to other breeds, and the Italian greyhound—the
2.5
3.0
Nem = 0
Nem = 0.25
Nem = 0.5
Empirical estimate (India wolf)
95% CI
1.5
0.5
0.6
0.7
Sw Sd
0.8
0.9
Nem = 0
Nem = 0.25
Nem = 0.5
Empirical estimate (India wolf)
95% CI
2.0
1.0
B
1.0
0.4
A
0
10000
20000
30000
40000
50000
0
10000
20000
30000
40000
50000
FIG. 6. The effect of assuming different migration rates (Nem) between dogs and wolves on the divergence time. The results are obtained from
simulations of a model of dog demographic history (see Materials and Methods). (A) The effect on the fraction of concordant genealogies and
(B) the effect on the relative TMRCA of dog and wolf sequences to the boxer genome (Sw/Sd).
1513
FIG. 5. Relative log-likelihood estimates of divergence time T between different dog breeds and wolves to the boxer/poodle ancestral
population. (A) Divergence between individual dog breeds (color indicates classification by Parker et al. [2004]) and wolf populations and (B)
joint divergence between canid populations and the ancient wolf. Dashed line represents the 95% CI cutoff.
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FIG. 7. Results of simulations of a potential divergence between the Altai wolf and the ancestral dog population. (A) Fraction of concordant
topologies for the Altai wolf compared with modern dogs and (B) relative average TMRCA between the Altai wolf and modern dog genomes
(SAltai/Sd). The age of the Altai remains is shown by a solid vertical line, and the empirically estimated values with a horizontal dashed line, with
the 95% CI indicated by gray shading.
Discussion
The probability of concordant or discordant genealogies
has been treated in the literature (e.g., Hudson 1983;
Takahata 1989; Rosenberg 2002; Wakeley 2008) but has
mainly been used in different methods to estimate ancestral effective population sizes in primate evolution (e.g.,
Chen and Li 2001; Yang 2002; Hobolth et al. 2007). To
our knowledge, the approach has previously not been used
to infer divergence times from nonoverlapping sets of shotgun sequences. The use of this summary statistic is robust
to a number of problems associated with evolutionary analysis of aDNA data. For instance, due to only utilizing information from mutations occurring on the internal branches
of genealogies of three sequences (plus the outgroup),
a postmortem mutation or sequencing error must confer
a change from a derived variant to the allele present in the
outgroup sequence to affect the outcome of the analysis.
Although we have illustrated that utilizing mutations confers a bias if genealogies in the concordant and discordant
classes have different average lengths of the internal branch
and that this effect is stronger if the internode time T is
much greater than Ne in the ancestral population, the bias
can be accounted for with simulations (fig. 4). Only utilizing
information on the internal branch also makes the approach appropriate for dealing with samples from different
time points (Figs 1 and 7A). In practice, inferring the genealogy of a sample of sequences requires that some mutation event happened on the internal lineages, and we only
need to assume that the mutation rate is equal for all lineages. In principle, this makes it possible to jointly consider
markers with different mutation rates (e.g., SNPs and in1514
dels), but without a closely related outgroup sequence
the states of indels are difficult to determine, a problem
that might be smaller for other studies (e.g., chimpanzee-human). Indeed, the use of a closely related outgroup
genome is likely to improve most population genetic estimates from ancient genomic data (Prüfer et al. 2010), but
we have shown that appropriate corrections can alleviate
biases introduced by sequencing errors (table 2) and short
fragment length (fig. 8A), even for rather distant genome
comparisons such as between cats and canids.
We obtained estimates of divergence time between wolf
and dog populations using a methodological framework that
is computationally flexible and robust to problems such as
time-structured sampling. Assuming no gene flow between
wolves and dogs after domestication, our results indicate
a divergence between dogs and wolves at least 10,000 years
ago (CI: 9,000–13,000), a conclusion that follows from assuming an ancestral effective population size (Ne) of
;13,000 chromosomes and a generation time of 3 years
(Lindblad-Toh et al. 2005; Gray et al. 2009). This number
is consistent with some previous estimates based on a divergence model with complete isolation between the populations (e.g., Savolainen et al. 2002; Gray et al. 2009). However,
several studies have documented hybridization between
gray wolves and dogs in sympatric regions (Randi 2008),
and this interbreeding may have been even more extensive
in the past (Vilá et al. 2005; vonHoldt et al. 2010). For instance, 5% of all samples from an encroached Italian wolf
population had admixed ancestry despite showing lupine
mtDNA and Y-haplotypes (Verardi et al. 2006).
Unlike previous analyses (e.g., Vilà et al. 1997; Savolainen
et al. 2002; Lindblad-Toh et al. 2005; Gray et al. 2009; Pang
et al. 2009), we also consider the effect of gene flow after
the domestication of dogs using an explicit population divergence model with migration. Although we do not estimate the extent of hybridization, we used relatively
conservative population migration rates (Nem 5 0.25–
0.5), and found that gene flow between dogs and wolves
is consistent with a divergence ;14,000 (CI: 11,000–
18,000) to ;30,000 years ago (CI: 15,000–90,000), for the
respective migration rates. Although the exact choices of
only representative from the Herding breed cluster—
displayed the second largest divergence time from the
boxer–poodle ancestor, followed by most ‘‘Mastiff-type’’
breeds and finally most breeds from the ‘‘Modern European’’
cluster. Our analysis also included data from an English
Shepherd, a breed that to our knowledge has not been included in previous multilocus studies on population structure. We found that its inferred divergence time is most
similar to dogs from the Modern European/Hunting cluster.
MBE
migration rates in our simulations are merely examples, the
accumulating evidence of gene flow between wolves and
dogs in many parts of the world (e.g., vonHoldt et al.
2010) makes these observations hard to reconcile with
the hypothesis of an origin of dogs during the Neolithic
transition in East Asia suggested by Pang et al. (2009)
on the basis of mtDNA variation. Instead, our results could
be taken as support for the hypothesis that domestication
was instigated earlier in human history, as indicated by recent archaeological finds (e.g., Sablin and Khlopachev 2002;
Germonpré et al. 2009). More complex models incorporating bottlenecks and varying migration rates could possibly
also explain the observed data. However, previous analyses
have pointed to two important demographic events in the
history of modern dog breeds, a first bottleneck during domestication and a second one during breed formation
(Lindblad-Toh et al. 2005). A recent study on canid genetic
variation concluded that domestication conferred a bottleneck in the form of a contraction in effective size without
subsequent recovery (Gray et al. 2009), and we find support
for this model in contrasting our divergence estimates with
the average TMRCA between dogs and wolves (fig. 6).
In addition, genome-wide analyses of dogs and wolves
recently showed that Middle Eastern wolves probably contributed the major part of the ancestry of modern dogs
(vonHoldt et al. 2010). This is in agreement with our
estimates that Indian wolves are most closely related to
European dog genomes (followed by Chinese, Spanish,
and Alaskan wolves) (table 1), but unfortunately no sequence data from Middle Eastern wolves were available
for analysis. It is noteworthy that this rank order of divergence for wolves of different regions differs from what is obtained using a modified pairwise differences statistics (Sw/Sd
in our notation), an approach that is commonly used for
genomic aDNA (Green et al. 2006, 2009, 2010; Noonan
et al. 2006; Prüfer et al. 2010). Here, the Alaskan wolf was
closest (followed by Chinese, Spanish and Indian wolves,
table 2), which indicates that the topological method is able
to retrieve results more congruent with other sources of
information.
Our analysis of genomic data from a Pleistocene wolf
from Altai, Russia (dated to 40–50 Ka), could also provide
information about the ancestral wolf population. However,
we find that sequence and population divergence estimates between the Altai wolf and the modern dog genomes are difficult to explain by the age of the remains
alone (fig. 7). Instead, our results indicate that this individual was part of a wolf population separated from the population that is ancestral to modern gray wolves by ;90,000
years (CI: 75,000–110,000 years). This observation is compatible with previous molecular and morphological evidence for several divergent gray wolf populations in the
North American-Eurasian tundra during the Late Pleistocene (Leonard et al. 2007; Pilot et al. 2010) as well as extant
endemic wolf populations (Sharma et al. 2004), and the divergence time for the Altai wolf estimated here highlights
the possibility of regional discontinuity between extant and
ancestral wolf populations also in Central Asia.
Using nonoverlapping single-individual sequence data
from nine different dog breeds, we were also able to recover
previously identified patterns of higher-order population
clusters (Parker et al. 2004). We find estimates of divergence time that separates the Alaskan Malamute from European breeds, but the divergence time is surprisingly low
compared with the observed number of pairwise differences in the same data (see table 2 and Lindblad-Toh et al.
2005), which could indicate that the divergence of the Alaskan malamute occurred at a time when the effective population size of dogs was large compared with the effective
population size during the more recent period of breed
1515
FIG. 8. The effect of fragment length on estimates of population divergence and relative TMRCA between dogs and wolves. (A) Uncorrected
and corrected fraction of concordant topologies, (B) corrected Sw/Sd, and (C) uncorrected frequency of the two discordant topologies per
alignment. In each plot is data shown for four randomly sampled data subsets from a modern (Chinese) wolf of 10,000 sequences with
fragment length 35, 75, 150, and 250 bp, respectively, and the full Chinese wolf data set (mean fragment length 934 bp). In (B) and (C), observed
values for the Altai wolf (mean fragment length 40 bp) is shown for comparison. Error bars show 95% bootstrap CIs.
creation. Although the exact rank order of divergence between modern dog breeds is unresolved (vonHoldt et al.
2010), we found a high degree of correspondence between
our inferred divergence times for European breeds and previously inferred breed clusters (compare fig. 5A and results
in Parker et al. 2004, 2007, and vonHoldt et al. 2010). The
observation of negative divergence times is not entirely unexpected considering that the boxer and poodle belonged
to separate population clusters in previous studies (e.g.,
Parker et al. 2004, 2007; vonHoldt et al. 2010), and that
the extremely low Ne in modern breeds (Sutter et al.
2004; Lindblad-Toh et al. 2005) causes the coalescent time
scale to be up to 10 times faster in the last 200–300 years
compared with the prehistoric population (Clutton-Brock
1987, 1995; Lindblad-Toh et al. 2005; Gray et al. 2009).
Conclusion
Acknowledgments
We are grateful to Benoit Nabholz for helpful computational suggestions and to Tom Gilbert, Eske Willerslev,
and two anonymous reviewers for valuable comments
on a previous version of the manuscript. We also wish
to thank Matthew Blow and Edward Rubin for kindly providing ancient wolf data. This work was supported by a Sven
and Lilly Lawski Foundation for Natural Sciences scholarship to P.S. and a grant from the Swedish Research Council
FORMAS to M.J. A.G. was supported by the Royal Swedish
Academy of Science while participating in this study. Computations were performed on Uppsala Multidisciplinary
Center for Advanced Computational Science (UPPMAX)
resources under project p2009038.
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MBE

Estimation of Population Divergence Times from Non

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